Chiral anomalies in supersymmetric theories

The supersymmetric non-abelian chiral anomaly is computed in a theory of chiral scalar superfields coupled to external gauge superfields, both in a vector-current conserving scheme and in a left-right symmetric scheme. The corresponding supersymmetric Wess-Zumino term is discussed; in particular we give an explicit expression for the anomalous bosonic term.     

Anomalous gauge theories as constrained Hamiltonian systems

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear σ-model and later for fermionic theory. The breakdown of the Gauss law constraints and the anomalous commutators among them are studied in a systematic way. An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints. Dirac brackets between the time components of gauge fields are shown to involve anomalous terms. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.     

Exact calculation of the Fermion determinant in chiral QCD2 reflecting the full regularization dependence

The fermion determinant of non-abelian anomalous gauge theory in two space-time dimensions is computed using the path-integral approach. The regularization dependence of the fermion determinant is worked out. Apart from a regularization dependentA ² term, the fermion determinant contains a Wess-Zumino-Witten anomaly functional.     

Anomalous inequivalence of phenomenological theories

When the transformation between bases in a phenomenological theory is anomalous, the theories are not equivalent, but can be made so by the addition of an appropriate anomaly functional. This functional can be given a simple form which allows the derivation of a sufficient condition for the impossibility of anomaly cancellation.     

Inversion of sequence of anomalies in core-softened systems with attraction

In this paper we present a simulation study of water-like anomalies in a purely repulsive core-softened system and in a system with attraction described in our previous publications. We investigate the anomalous regions for systems with the same functional form of the potentials but with different parameters and show that the order of the region of anomalous diffusion and the region of density anomaly is inverted with increasing the width of the repulsive shoulder and the depth of the attractive well. It is shown that while the density anomaly is always inside the region of the structural anomaly, the diffusion anomaly can change its location depending on the parameters of the potential. In the presence of the attraction in the potential, the system demonstrates the silica-like behavior.     

Hamiltonian Anomalies from Extended Field Theories

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Quantum measurements and chiral magnetic effect

The effect of anisotropy for fluctuations of electric currents in magnetic field is addressed within framework of quantum measurements theory. It is shown that for free fermions in uniform magnetic field the anisotropy is of the same sign as one expects for chiral magnetic effect and is related to triangle anomaly. The corresponding decoherence functional contains anomalous off-diagonal terms leading to correlation of fluctuations between observables of opposite P-parity.     

Trace anomalies and λφ4 theory in curved space

It is shown for a conformally invariant λφ⁴ theory in a weakly curved background, how to extend previous results to obtain full information about the trace anomaly in perturbation theory, including the “topological” term in the gravitational part of the anomaly. There is a strong connection among renormalisability of the curved space theory, finiteness of the energy-momentum tensor, and the role of normal products. Combined with a renormalisation-group analysis this provides an efficient means of calculating some terms in the anomaly to high orders of perturbation theory. In particular, the first λ-dependent coefficient of the topological part of the anomaly appears at O(λ⁴) and can be deduced from simple flat-space results without the calculation of any further Feynman diagrams. Some techniques based on an absorptive-part argument are developed in order to compute other anomalous coefficients, and a direct 5-loop calculation confirms the indirect renormalisation-group derivation of a non-vanishing R² anomaly at O(λ⁵). All the essential information can be obtained from the massless theory. The underlying ideas are applicable to other theories, and similar results for massless QED are obtained in a subsequent paper.     

The aetiology of sigma model anomalies

Certain nonlinear sigma models with fermions are ill-defined due to an anomaly which exhibits characteristics of both the nonabelian gauge theory anomaly and the SU(2) anomaly. The simplest way to diagnose the anomaly involves consideration of the global topology of the theory. We review the mathematical methods needed for this analysis and apply them to several supersymmetric sigma models. Some of these are found to be anomalous.     

The structure of anomalies for arbitrary dimension of the space-time

The construction of anomalies in Ward identities is investigated for arbitrary dimension of the space-time. If the internal symmetry group is semi-simple and compact we find that for even dimension of the space-time the anomalous term is unique and that no anomaly is constructible for odd dimension.     

The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so-called Proton Spin Problem. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated U_A(1) anomaly. This anomaly is intimately associated with the η′ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the U_A(1) anomaly is known to induce color anomaly leading to “leakage” of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This “color boundary term” inherits part or most of the dynamics of the volume (i.e., QCD). In this paper, we exploit this mapping of the volume to the surface via the color boundary condition to perform a complete analysis of the flavor singlet axial charge in the chiral bag model using the Cheshire Cat Principle. This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor singlet axial charge is small independent of the confinement (bag) size ranging from the skyrmion picture to the MIT bag picture, thereby confirming the (albeit approximate) Cheshire Cat phenomenon.     

Windows over a new low energy axion

We outline some general features of possible extensions of the Standard Model that include anomalous U(1)$U(1)$ gauge symmetries, a certain number of axions and their mixings with the CP-odd Higgs sector. As previously shown, after the mixing one of the axions becomes a physical pseudoscalar (the axi-Higgs) that can take the role of a modified QCD axion. It can be driven to be very light by the same non-perturbative effects that are held responsible for the solution of the strong CP-problem. At the same time the axi-Higgs has a sizeable gauge interaction, which is not allowed to the Peccei–Quinn axion, possibly explaining the PVLAS results. We point out that the Wess–Zumino term, typical of these models, can be both interpreted as an anomaly inflow from higher dimensional theories (second window) but also as a result of partial decoupling of an extra Higgs sector (and of a fermion) that leaves behind an effective anomalous Abelian theory (first window) in a broken Stückelberg phase. The possibility that the axi-Higgs can be heavy, of the order of the Higgs mass or larger, however, cannot be excluded. The potentialities for the discovery of this particle and of anomaly effects in the neutral current sector at the LHC are briefly discussed in the context of a superstring inspired model (second window), but with results that remain valid also if any of the two possibilities is realized in Nature.     

Scalar form factors and nuclear interactions

The scalar-isoscalar term in the two-pion exchange NN potential is abnormally large and does not respect the hierarchy of effects predicted by chiral perturbation theory. We argue that this anomaly is associated with non-perturbative effects, which are also present in the πN scalar form factor.     

The anomalous effective action in three-dimensional gauge theories

Summary We analyse the effective action for gauge fields in odd dimensions, obtained by integrating out the fermions in the Feynman path integral. In particular, we discuss the generation of a Chern-Simons term by massless fermions minimally coupled to an Abelian gauge field. We review two methods of revealing the presence of a Chern-Simons term in the effective action: first, as the consequence of a nontrivial holonomy of the fermionic ground state, then as the result of the generation of an anomalous imaginary part of the effective action. We derive the most general form of the anomalous effective action at the lowest nontrivial order of a derivative expansion in time. We discuss the implications of our analysis for the theory of the fractional quantum Hall effect as well as for the quantization of anomalous theories. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Generalized Chern–Simons modified gravity in first-order formalism

We propose a generalization of Chern–Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences.     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

On the quantization of anomalous theories

The possible definition of the Gauss' law operator in an anomalous gauge theory is discussed. It is shown that the most natural choice does not lead to any anomaly in the commutation rules. The case of two-dimensional theories is considered.     

Hamiltonian formulation of the anomalous chiral Schwinger model

We construct the hamiltonian formulation of the anomalous chiral Schwinger model, which has recently been shown to yield a consistent unitary theory. The impact of the anomaly on the constraints of the system is exhibited and the system is quantized using an appropriate hamiltonian consistent with the constraints.     

THE UNIFIED SCHEME OF THE EFFECTIVE ACTION AND CHIRAL ANOMALIES IN ANY EVEN DIMEPISIONS

Based on the Weil homomorphism method, a unified scheme in which all the important topological ptoperties of the pseudoscalar Goldstone bosonand gauge fields. in even dimensional space are described, in one remarkably compact. form is given.These properties include the effective action, the skyrmion anomalous current, Abel'an anomaly, symmetric and asymmetric non-Abeliari chiral anomalies,and anomaly free conditions.